When the person is at the top of the slide they have lots of gravitational potential energy, but no kinetic energy (they aren't moving). As they begin to slide down, that gravitational potential energy is converted into kinetic energy. Remember that K=1/2mv^2. Since the height of the slide does not change, our potential energy is the same in both cases, which means that our kinetic energy must also be the same. Assuming it is the same person sliding down the slide, and that they didn't just go pig out at the buffet, their mass is also the same. According to our equation, if the kinetic energy is the same, the mass is the same, then the speed at which the slider leaves the slide must be the same.

In 9.), there is friction between the block and the ramp, so in addition to doing work on the box to increase its potential energy, work has to be done to move the box against the force of friction. The work done to move the box vertically to increase its potential energy is the same for both cases: they are both lifted h distance. However, the friction force acts against moving the block across the ramps surface, and is equal to the coefficient of friction times the normal force (Ffric = mu*N). When the angle of inclination decreases, the normal force N on the block by the ramp increases (N=mgcos(theta)), and therefore the friction force increases. The work done on the block by the friction force is Work = mu*N*X, where X is the distance moved across the ramp. Since the second ramp has a longer distance for the block to move across to reach the same height, the friction force acts for a longer distance, and more work has to be done on the block to reach the top.